Properties

Label 108900.f
Number of curves 4
Conductor 108900
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("108900.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 108900.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
108900.f1 108900ct4 [0, 0, 0, -193306575, -1034470170250] [2] 14929920  
108900.f2 108900ct3 [0, 0, 0, -12124200, -16044040375] [2] 7464960  
108900.f3 108900ct2 [0, 0, 0, -2731575, -981945250] [2] 4976640  
108900.f4 108900ct1 [0, 0, 0, -1234200, 516927125] [2] 2488320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 108900.f have rank \(0\).

Modular form 108900.2.a.f

sage: E.q_eigenform(10)
 
\( q - 4q^{7} - 4q^{13} + 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.